This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Determine the equivalent resistance for parallel resistors. The resistors R and X are connected in parallel. The equivalent resistance R_eq is given by: R_eq = (R · X)/(R + X) Step 2: Apply Ohm's Law. The total voltage E across the parallel combination is constant. According to Ohm's Law, E = I · R_eq, where I is the total current measured by the ammeter. Substituting the expression for R_eq: E = I · (R · X)/(R + X) Step 3: Use the first set of data to form an equation for E. When R = 5 \, , the current I = 3 \, A. E = 3 \, A · (5 \, · X)/(5 \, + X) E = (15X)/(5 + X) (*) Step 4: Use the second set of data to form another equation for E. When R = 2 \, , the current I = 6 \, A. E = 6 \, A · (2 \, · X)/(2 \, + X) E = (12X)/(2 + X) (**) Step 5: Equate the two expressions for E and solve for X. Since E is constant, we can set equation () equal to equation (*): (15X)/(5 + X) = (12X)/(2 + X) Assuming X ≠ 0 (as X is a resistance), we can divide both sides by X: (15)/(5 + X) = (12)/(2 + X) Cross-multiply: 15(2 + X) = 12(5 + X) 30 + 15X = 60 + 12X Subtract 12X from both sides: 30 + 15X - 12X = 60 30 + 3X = 60 Subtract 30 from both sides: 3X = 60 - 30 3X = 30 Divide by 3: X = (30)/(3) X = 10 \, The value of X is 10 \, . This corresponds to option C. The final answer is C. 10 ohms.